PySimple1Gen OpenSees Command

Transcription

1 PySimple1Gen OpenSees Command By: Scott Brandenberg Date: June 28 th, 2004 PySimple1Gen $File1 $File2 $File3 $File4 $File5 <$File6> The PySimple1Gen command constructs PySimple1 materials (Boulanger, 2003) for predefined zerolength elements The command requires five arguments, and supports an optional sixth argument, all of which are file names The first file contains soil and pile properties required to define the PySimple1 materials The second file contains information about the nodes that define the mesh The third file contains information about the zerolength elements that are to be assigned PySimple1 materials (hereafter called p-y elements) The fourth file contains information about the beam column elements that are attached to p-y elements The fifth file is the output file to which the PySimple1 materials are written The sixth file is the output file to which the applied patterns are written (optional) The command has been structured such that File2, File3, File4, File5 and File6 can be sourced directly by OpenSees from within a master tcl file Hence File2, File3 and File4 serve two purposes: 1 They provide information to PySimple1Gen to create the PySimple1 materials 2 They can be sourced directly in a master tcl file to define the nodes, zerolength elements for p-y materials, and pile elements, respectively Furthermore, File5 and File 6 serve the following purpose: 1 They can be sourced by OpenSees from within a master tcl file to define the PySimple1 materials and the applied patterns, respectively The intended use of the files is demonstrated in an example problem in the Appendix

2 File1 The first input file, File1, contains soil and pile properties that are required to calculate the material properties for the PySimple1 materials, and optional information about p-multipliers, and applied patterns (either loads on the pile nodes, or displacements on the free ends of the p-y elements) Optional information is placed inside angle brackets (ie < Optional Information >) The format of File1 is as follows: mattype(1) z_t(1) z_b(1) γ _t(1) γ _b(1) Additional Arguments(1) mattype(n) z_t(n) z_b(n) γ _t(n) γ _b(n) Additional Arguments(N) <sp or load zpattern_t(1) zpattern_b(1) PatternVal_t(1) PatternVal_b(1) sp or load zpattern_t(n) zpattern_b(n) PatternVal_t(N) PatternVal_b(N) mp zmp_t(1) zmp_b(1) MpVal_t(1) MpVal_b(1) mp zmp(n) zmp_b(n) MpVal_t(N) MpVal_b(N)> where, b = pile diameter (meters) zground = z-coordinate of ground surface (meters) NPile = number of piles out-of-plane (if the analysis is in the y-z plane, then NPile is the number of piles along the x-axis) mattype = py1 mattype = py2 mattype = py3 mattype = py4 Approximates Matlock s (1970) soft clay p-y relation Approximates API (1993) sand p-y relation Liquefied sand with normalized mobilized liquefied strength ratio (approximates API sand shape) Nonliquefied crust over liquefied sand relation (approximates either Matlock soft clay p-y relation or API sand relation) z_t = z-coordinate of top of sub-layer (meters) z_b = z-coordinate of bottom of sub-layer (meters) γ _t = buoyant unit weight at top of sub-layer (kn/m 3 ) γ _b = buoyant unit weight at bottom of sub-layer (kn/m 3 ) 2/17

3 Additional arguments are required for each different material (ie each different mattype), as summarized below: mattype = py1 Matlock (1970) soft clay p-y relation AdditionalArguments = b_t b_b cu_t cu_b e50_t e50_b Cd_t Cd_b <c_t c_b> b_t = pile diameter (m) at depth z_t b_b = pile diameter (m) at depth z_b cu_t = undrained shear strength (kpa) at depth z_t cu_b = undrained shear strength (kpa) at depth z_b e50_t = shear strain at 50% shear stress for clay at depth z_t e50_b = shear strain at 50% shear stress for clay at depth z_b Cd_t = drag coefficient at depth z_t Cd_b = drag coefficient at depth z_b c_t = viscous damping term (optional) on the far-field (elastic) component of the displacement rate (velocity) at depth z_t (00 default) c_b = viscous damping term (optional) on the far-field (elastic) component of the displacement rate (velocity) at depth z_b (00 default) mattype = py2 API (1993) sand p-y relation AdditionalArguments = b_t b_b phi_t phi_b Cd_t Cd_b <c_t c_b> b_t = pile diameter (m) at depth z_t b_b = pile diameter (m) at depth z_b phi_t = friction angle (degrees) at depth z_t phi_b = friction angle (degrees) at depth z_b Cd_t = drag coefficient at depth z_t Cd_b = drag coefficient at depth z_b c_t = viscous damping term (optional) on the far-field (elastic) component of the displacement rate (velocity) at depth z_t (00 default) c_b = viscous damping term (optional) on the far-field (elastic) component of the displacement rate (velocity) at depth z_b (00 default) mattype = py3 Liquefied sand with normalized residual strength ratio p-y relation AdditionalArguments = b_t b_b phi_t phi_b S/σ v _t S/σ v _b ru_t ru_b Cd_t Cd_b <c_t c_b> b_t = pile diameter (m) at depth z_t b_b = pile diameter (m) at depth z_b phi_t = friction angle (degrees) at depth z_t (used only to calculate y 50 ) phi_b = friction angle (degrees) at depth z_b (used only to calculate y 50 ) S/σ v _t = residual strength ratio at depth z_t at r u = 10 S/σ v _b = residual strength ratio at depth z_b at r u = 10 ru_t = peak excess pore pressure ratio at coordinate z_t ru_b = peak excess pore pressure ratio at coordinate z_b 3/17

4 Cd_t = drag coefficient at coordinate z_t Cd_b = drag coefficient at coordinate z_b c_t = viscous damping term (optional) on the far-field (elastic) component of the displacement rate (velocity) at depth z_t (00 default) c_b = viscous damping term (optional) on the far-field (elastic) component of the displacement rate (velocity) at depth z_b (00 default) mattype = py4 User-specified p ult and y ult AdditionalArguments = type p ult _t p ult _b y 50 _t y 50 _b Cd_t Cd_b <c_t c_b> type = 1 for approximation of Matlock s (1970) soft clay p-y relation type = 2 for approximation of API (1993) sand p-y relation p ult _t = ultimate capacity of p-y element (kn/m) at depth z_t p ult _b = ultimate capacity of p-y element (kn/m) at depth z_b y 50 _t = relative displacement (soil displacement minus pile cap displacement) at which 50% of ultimate resistance is reached in a monotonic virgin loading cycle at depth z_t (meters) Y 50 _b = relative displacement (soil displacement minus pile cap displacement) at which 50% of ultimate resistance is reached in a monotonic virgin loading cycle at depth z_b (meters) Cd_t = drag coefficient at depth z_t Cd_b = drag coefficient at depth z_b c_t = viscous damping term (optional) on the far-field (elastic) component of the displacement rate (velocity) at depth z_t (00 default) c_b = viscous damping term (optional) on the far-field (elastic) component of the displacement rate (velocity) at depth z_b (00 default) Applied Patterns sp is a character tag identifying the subsequent fields on the line as defining a displacement pattern assigned to the free ends of the p-y elements load is a character string identifying the subsequent fields on the line as defining a load pattern assigned to the pile nodes zpattern_t = z-coordinate of top of applied displacement or load (meters) zpattern_b = z-coordinate of bottom of applied displacement or load (meters) PatternVal_t = applied incremental displacement (meters) or load pattern (kn/m) at coordinate zpattern_t PatternVal_b = applied incremental displacement (meters) or load pattern (kn/m) at coordinate zpattern_b P-Multipliers mp is a character string identifying the subsequent fields on the line as defining a p-multiplier zmp_t = z-coordinate of top of p-multiplier distribution (meters) zmp_b = z-coordinate of bottom of p-multiplier distribution (meters) MpVal_t = p-multiplier at coordinate zmp_t MpVal_b = p-multiplier at coordinate zmp_b 4/17

5 File2 The second input file, File2, contains information about the nodes that define the pile elements and the zerolength elements that are to be assigned PySimple1 materials The format of File2 is as follows: node nodenum(1) y(1) z(1) node nodenum(n) y(n) z(n) where, nodenum = number of node y = y-coordinate of node z = z-coordinate of node File3 The third input file, File3, contains information about the zerolength elements that are to be assigned PySimple1 materials The format of File3 is as follows: element zerolength elenum(1) node1(1) node2(1) mat mattag (1) <ExtraInput> element zerolength elenum(n) node1(n) node2(n) mat mattag (N) <ExtraInput> where, elenum = element number node1 = a node defining the zerolength element node2 = a node defining the zerolength element mattag = material tag to be associated with a PySimple1 material ExtraInput is an optional text string that comes after mattag The reason for allowing ExtraInput is to facilitate dual use of File3 in both the PySimple1Gen command, and in a master tcl file as demonstrated in the Appendix 5/17

6 File4 The fourth input file, File4, contains information about the pile elements to which the p-y elements connect This file is required to calculate the tributary length required to define each PySimple1 material, and for applying load patterns to pile nodes The format of File4 is as follows: element elementtype elenum(1) node1(1) node2(1) <ExtraInput> element elementtype elenum(n) node1(n) node2(n) <ExtraInput> elenum = element number node1 = a node defining the pile element node2 = a node defining the pile element ExtraInput is an optional text string that comes after mattag The reason for allowing ExtraInput is to facilitate dual use of File4 in both the PySimple1Gen command, and in a master tcl file as demonstrated in the Appendix File5 The output file, File5, contains the PySimple1 materials The format of File5 is as follows: #################################################################### ## Start PySimple1 Materials uniaxialmaterial PySimple1 mattag(1) pytype(1) P ult (1) y 50 (1) Cd(1) c(1) uniaxialmaterial PySimple1 mattag(n) pytype(n) P ult (N) y 50 (N) Cd(N) c(n) ## End PySimple1 Materials ##################################################################### where, mattag = material tag associated with the corresponding zerolength element soiltype = 1 Backbone of p-y curve approximates Matlock (1970) soft clay relation soiltype = 2 Backbone of p-y curve approximates API (1993) sand relation P ult = capacity of PySimple1 material (kn) y 50 = relative displacement at 05p ult (m) Cd = drag coefficient c = viscous damping term (optional) on the far-field (elastic) component of the displacement rate (velocity) 6/17

7 File 6 File 6 contains the Pattern that applies loads to the pile nodes, and/or displacements to the free ends of the p-y elements The format of File6 is as follows: #################################################################### ## Begin Pattern File load nodenum ForceValue load nodenum ForceValue sp nodenum 1 DisplacementValue sp nodenum 1 DisplacementValue ## End Pattern File #################################################################### Note that p-y elements are assumed to be oriented in the 1-direction, so the patterns are applied in the 1-direction File Format The format of File1 must be strictly followed to prevent I/O error Metadata and comment lines are not permitted for File 1 For cases in which both patterns (ie sp or load ) and p- multipliers (ie mp ) are applied, they may be specified in any order (ie p-multipliers may be intermixed with applied loads and displacements) For File2, data is read for each line that begins with node and other lines are ignored For File3 and File4, data is read for each line that begins with element and other lines are ignored Hence, extra data and blank rows are permitted for File2, File3, and File4 as long as rows that contain irrelevant data do not begin with the string node for File2 or element for File3 and File4 The output files, File5 and File6, contain a header that explains that the PySimple1Gen program was used to create the file The PySimple1Gen command does not contain the functionality of tcl For example, the programming features of tcl allow nodes to be defined using a loop, as demonstrated below: # Create pile nodes, with double nodes for adding zerolength soil springs for {set i 0}{$i<=30}{incr i 1}{ set ydim1 [expr $i*$dy1-660] node [expr $i*2+1] 0 $ydim1 node [expr $i*2+2] 0 $ydim1 node [expr $i*2+63] -$dx $ydim1 node [expr $i*2+64] -$dx $ydim1 node [expr $i*2+125] $dx $ydim1 node [expr $i*2+126] dx $ydim1 } 7/17

8 However, PySimple1Gen cannot recognize such loops The node number and nodal coordinates must be numbers for PySimple1Gen; expressions are not permitted Linear Interpolation At a given node, soil properties, p-multipliers and displacement patterns are linearly interpolated based on the location of the node and the location and associated soil properties and pattern values defined in File1 Distributed loads along the pile are integrated over the tributary length to obtain nodal loads A node will be assigned a load pattern if any part of its tributary area overlaps with any part of the applied distributed load, even if the node itself lies outside of the region in which distributed loads were defined P-y elements lying outside of the region of defined p-multipliers will be assigned a p-multiplier of 10 8/17

9 APPENDIX 1: EXAMPLE PROBLEM An example problem has been constructed to show how the structure of the input and output files relates to a simple soil-pile model The purpose of the example problem is to illustrate much of the functionality of the PySimple1Gen command, and not to accurately model the response the pile The small number of p-y elements in the example problem is likely insufficient to result in an accurate solution, but permits a clear means of demonstrating the function of the PySimple1Gen command The extended pile shaft shown in Figure 1 is composed of six beam column elements, and penetrates a soil profile consisting of clay overlying sand The clay layer deforms under uniform shear strain such that its surface displacement is 02 m, and the sand layer exhibits no displacement Additionally, a distributed load is applied to the top portion of the shaft above the ground surface Material properties are shown in the figure 6 z (m) 3 25 kn/m m Clay 3 γ' = 7 kn/m cu = 40 kpa ε 50= 001 Cd = 01 c = Pile b = 05 m E = 200 GPa 2 A = 0017 m 4 I = m Sand γ' = 10 kn/m φ = 36 deg Cd = 01 c = 15 mp = Figure 1: Example problem to illustrate PySimple1Gen command 9/17

10 File1: Soil Properties Input File SoilProptcl py py load sp sp mp File2: Nodes Input File Nodestcl ############################################################# ## Begin Nodes node node node node node node node node node node node node ## End Nodes #################################################################### File3: Py Elements Input File PyElementstcl ############################################################### ## Begin p-y elements element zerolength mat 5 dir 1 element zerolength mat 17 dir 1 element zerolength mat 19 dir 1 element zerolength mat 23 dir 1 element zerolength mat 7 dir 1 ## End p-y elements ################################################################### Note that the material tags (-mat??) have been assigned arbitrarily The PySimple1Gen command will use the arbitrary material tag to construct a PySimple1 material that is associated with the proper element 10/17

11 File4: Pile Elements Input File PileElementstcl ############################################################### ## Begin beam-column elements element elasticbeamcolumn element elasticbeamcolumn element elasticbeamcolumn element elasticbeamcolumn element elasticbeamcolumn element elasticbeamcolumn ## End beam-column elements #################################################################### File5: Py Materials Output File PyMaterialstcl #################################################################################### ## Material Properties for py Elements uniaxialmaterial PySimple uniaxialmaterial PySimple uniaxialmaterial PySimple uniaxialmaterial PySimple uniaxialmaterial PySimple ## End Material Properties for py Elements #################################################################################### The material tags (ie the first number after the string Pysimple1) are the same tags that were previously assigned arbitrarily to the zerolength elements File6: Pattern Output File Patterntcl #################################################################################### ## Begin Pattern File sp sp sp sp sp load load ## End Pattern File #################################################################################### 11/17

12 Implementation in master tcl file PySimple1Gen has be structured to receive certain arguments that are not required to define the p-y materials (ie ExtraInput ), but are required to define the nodes and elements in OpenSees So, as a matter of convenience, PySimple1Gen reads fields that are not essential to its function so that the files can serve two purposes: 1 They can be used arguments for the PySimple1Gen command 2 They can be sourced directly from a master tcl script file to define nodes and elements For the example problem, assume that the input files (File1 through File4) required as arguments for PySimple1Gen are contained in the same folder as the master tcl file, and their file names are as follows: File1: SoilProptxt File2: Nodestcl File3: PyElementstcl File4: PileElementstcl Furthermore, assume that the output files (File5 and File6) are named: File5: PyMaterialstcl File6: Patterntcl Using the preceding information, the following master tcl file utilizes the files in the PySimple1Gen command, and also to define the nodes and elements in the domain ####################################################################### # Master file for py pushover analysis to illustrate PySimple1Gen # command # # Created by Scott Brandenberg, April 30, 2004 ####################################################################### wipe set NumSteps 100 set StepSize [expr 10/$NumSteps] ############################################################# # BUILD MODEL # model basic -ndm 2 -ndf 3 # define the nodes source Nodestcl # create geometric transformation for pile elements geomtransf Linear 1 12/17

13 # define pile elements source PileElementstcl # use PySimple1Gen command to generate PyMaterialstcl and Patterntcl PySimple1Gen "SoilProptxt" "Nodestcl" "PyElementstcl" "PileElementstcl" "PyMaterialstcl" "Patterntcl" # define py elements and materials Always define materials before # elements to prevent input error Note that PyMaterialstcl was previously created using the # PySimple1Gen command source PyMaterialstcl source PyElementstcl # Fix free ends of py elements against rotation and vertical displacement fix fix fix fix fix # Fix vertical deformation at pile tip fix ############################################################# # NOW APPLY LOADING SEQUENCE AND ANALYZE (plastic) # Create the pattern Note that Patterntcl was created using the PySimple1Gen command pattern Plain 1 Linear { source Patterntcl } #create the recorder recorder Node -file SoilDisplacementdat -time -node dof 1 2 disp recorder Node -file PileDisplacementdat -time -node dof 1 2 disp recorder Element -file PileElementRecorderdat -time -ele force recorder Element -file PyElementRecorderdat -time -ele force ############################################################# # create the Analysis constraints Penalty 1e12 1e12 test NormUnbalance 2e numberer RCM algorithm Newton system ProfileSPD integrator LoadControl $StepSize analysis Static ############################################################# # analyze analyze $NumSteps wipe #flush output stream 13/17

14 APPENDIX 2: TECHNICAL INFORMATION Calculating p ult and y 50 The ultimate resistances of the p-y materials p ult, were calculated in a manner similar to that described in LPile + 40m technical manual (Reese et al 2000) The difference between the method used in PySimple1Gen and in LPile + 40m involves the treatment of layered soil systems LPile + 40m utilizes the method developed by Georgiadis (1983) for calculating p ult for layered soils PySimple1Gen does not use the method of Georgiadis Instead, p ult is calculated based on the vertical effective stress at a given depth, with no consideration of the strength of overlying soil layers The equations used in PySimple1Gen are included below: For soft clay (pytype = 1) σ v ' 05 pu1 = c b c z pu2 = 9 c b p ult = min( pu1, pu2) where, σ v = vertical effective stress c = undrained shear strength z = depth b = pile diameter For sand (pytype=2) K o z tan( φ) sin( β ) pu1 = σ v ' + tan( β φ) cos( α) tan( β ) σ v ' tan( β φ) = min( pu1, pu2) ( b + z tan( β ) tan( α) ) + K z tan( β ) ( tan( φ) sin( β ) tan( α) ) K b 8 ( tan ( β ) 1) 4 pu2 = K b σ ' + K b σ ' tan( φ) tan ( β ) p ult a v o v o a 14/17

15 where, σ v = vertical effective stress Ko = coefficient of earth pressure at rest (default Ko = 04) φ = friction angle of sand β = 45 + φ/2 α = φ/2 z = depth b = pile diameter K a = coefficient of active earth pressure (K a = tan 2 (45 φ/2)) The relative displacement at 050p ult, y 50, is calculated in PySimple1Gen in the same way as discussed in the LPile + 40m technical manual For sand in LPile + 40m, stiffness, k, is an input parameter In PySimple1Gen, k is not an input parameter Instead, it is calculated from a polynomial curve fit of the relationship between friction angle and stiffness for sand above the water table provided in Figure 329 in the LPile + 40m technical manual For liquefied sand (pytype = 3) for r u = 0 (assuming undrained capacity with r u = 0 is the same as drained capacity) 1 K o z tan( φ) sin( β ) pu ru = σ ' + 0 v tan( β φ ) cos( α ) pu2 pu ru0 ru0 tan( β ) σ v ' tan( β φ) = K a b σ = min(pu1 v ru0 ( b + z tan( β ) tan( α) ) + K z tan( β ) ( tan( φ) sin( β ) tan( α) ) K b 8 ( tan ( β) 1) ', pu2 ru0 ) + K o b σ v o ' tan( φ) tan 4 ( β) a for r u = 1 pu ru1 = 9 S b for 0 < r u < 1 pu = pu where, ru0 + r u [ pu pu ] ru1 ru0 S = strength of sand mobilized against pile b = pile diameter r u = peak excess pore pressure ratio Ko = coefficient of earth pressure at rest (default Ko = 04) φ = friction angle of sand 15/17

16 β = 45 + φ/2 α = φ/2 z = depth b = pile diameter K a = coefficient of active earth pressure (K a = tan 2 (45 φ/2)) For user-specified (pytype = 4) p ult and y 50 are user-specified Tributary Length for p-y Elements The p-y material properties must contain P ult in units of force, not p ult in units of force/length P ult represents the integral of p ult over the tributary length The integration was performed numerically in the following manner: 1 z_top (coordinate at the top of the tributary length) and z_bot (coordinate at the bottom of the tributary length) were calculated as the midpoints of the pile elements that share a node with the p-y element, provided that the pile elements had a p-y element attached to its other node as well For example, pile elements that extend above the ground surface will not contribute any tributary length to a p-y element at or below the ground surface 2 The tributary length was divided into 10 sublayers, each with thickness, dz 3 P ult was calculated as the sum of p ult *dz over the ten sublayers from z_bot to z_top In the case when a p-y element lies near a boundary between two soil layers, such that its tributary length spans across the layer boundary, p ult will be based on properties of both soil layers due to numerical integration over the tributary length The type of p-y element (ie sand or clay) and y 50 will be based on the material properties at the p-y element location The numerical integration of p ult over the tributary length will reduce errors associated with interface effects, however closely spaced p-y elements are recommended at layer interfaces In the case when a p-y element lies at a boundary between two soil layers, the material type will be assigned the same type as the upper soil layer Tributary Length for Loads Applied to Pile Elements Tributary lengths for loads applied to pile elements are calculated in the same manner as for p-y elements, except that beam column elements that do not attach to p-y elements can contribute tributary length to the calculation of nodal loads For example, you may apply a distributed load to a beam column above the ground surface without any attached p-y elements (as was illustrated in the example) You may also apply a distributed load to a pile element with attached p-y elements 16/17

17 Error Checking 1 The program checks that all five (or six) files can be opened If not, the program will issue a warning and return without writing data to the output file(s) 2 The program checks that MatType = py1, py2, py3 or py4 If not, the program issues the following warning: Invalid MatType in PySimple1Gen, and then exits without writing data 3 The program checks that the depth of each node lies within the depths specified in the soil properties file (File1) If not, a warning is issued and vertical stress is set to zero APPENDIX 3: REFERENCES API(1993) Recommended Practice for Planning, Design, and Constructing Fixed Offshore Platforms API RP 2A - WSD, 20 th ed, American Petroleum Institute Boulanger, R W (2003) The PySimple1 Material Georgiadis, M (1983) Development of p-y curves for layered soils Proc, Geotechnical Practice in Offshore Engineering, ASCE, pp Matlock, H (1970) Correlations of design of laterally loaded piles in soft clay Proc Offshore Technology Conference, Houston, TX, Vol 1, No1204, pp Reese, L C, Wang, S T, Isenhower, W M, Arrelaga, JA, and Hendrix, J A (2000) LPILE Plus Verion 40m, Ensoft, Inc Austin, TX 17/17